Alternatively, let’s say education signals IQ or some other notion of “smarts.” On-line education would seem to offer less opportunity to get through by buttering up the teacher, spouting mumbo-jumbo in basket-weaving classes, and so on. For better or worse, a lot of on-line education seems to be based on relatively objective tests. Then on-line education would seem to offer a better signal of smarts.

I am always amazed to see a complicated looking mathematical derivation starting from a fundamentally flawed assumption (all too common in the social sciences IMNSHO, I think this technique is used to intimidate those who are impressed by complicated math). Bryan Caplan's model is a classic example of this. He starts off by assuming "Intelligence is uniformly distributed between A and 100+A" which is ridiculous. IQ is roughly a Gaussian distribution with mean 100 and SD ~15. (even if one doesn't grant that intelligence ~= IQ I think it is hard to argue that intelligence is not something close to a Gaussian) It is possible this makes no difference to the analysis, but a uniform distribution and a Gaussian distribution are very different. For reference, direct link to his original post: http://econlog.econlib.org/archives/2012/04/is_rising_educa.html

@robrambusch I upvoted you because I thought some of the discussion in your link was good (and appreciated being pointed to the conversation), but given Caplan's assumption I'm not even willing to spend the time trying to follow his analysis. Sometimes overly simplistic models can be helpful understanding the world (the Model Thinking class makes this point repeatedly, and it is a good one), but discerning whether or not this is the case can be hard work. Sometimes overly simplistic models are unhelpful (or even detract from understanding by leading to incorrect conclusions).

@rseiter - I'll go out on a limb here and agree with you ("He starts off by assuming "Intelligence is uniformly distributed between A and 100+A" which is ridiculous."). My guess is that when Charles Murray goes to the trouble of writing a book on intelligence and titles it "The Bell Curve" that we can pretty much eliminate uniform distribution ;-)
Each participant completed the Armed Forces Qualifying Test (AFQT)--which, like any diverse test of mental ability, can be used as a measure of intelligence--and was then evaluated for subsequent social outcomes (including high-school graduation, level of income, likelihood of being in jail, likelihood of getting divorced, and so forth). As a rule, a person's intelligence turned out to predict such outcomes more strongly than did the socio economic status of his parents. This relationship held for all ethnic groups; indeed, when intelligence was statistically controlled, many "outcome" differences among ethnic groups vanished.
http://www.wjh.harvard.edu/~cfc/Chabris1998a.html

@rseiter
I didn't make it through the math but perhaps his argument relies more on symmetry around the mean rather than uniformity around the mean? Hopefully calling it uniform was just a slip up, since I'm not sure economists know much else beyond gaussians.
In general I'm pretty sympathetic to attributing most of the value of higher education to signaling rather than the intrinsic value of knowledge (particularly outside of STEM), largely from knowing a liberal arts graduate or two.
--the philosophy major

@beard I'm pretty sympathetic to the signalling argument as well. In that respect it is interesting to note the declining average IQ of college grads since the 1950's. I think in a depressingly real way the college diploma has become the new (very expensive) high school diploma (yes, I am exaggerating, but if one listens to professors talk about how much "remedial" material is required for incoming students I'm not sure by how much). Economists are interesting because some approach the field from a mathematical perspective and some approach it from a social science philosophy (with many shades of gray in between of course).
Based on the math Caplan really is assuming a uniform distribution. He is very explicit with the terminology "IQ ~ U[A, 100+A]" and if you look at the integral it is clear he is not using a gaussian (I suspect he does this to make the math easier).
I can be hard on bad arguments advanced in favor of things I believe because I believe they weaken the message and make it far too easy to rebut. To be clear, Caplan using overly simple math does not indicate the signalling theory is wrong, but it also does not support it.

Here's a quote from a later post on the same topic (signaling):
In the interest of parsimony, my model assumes that education is purely a signal of IQ; Tyler also considers a variant where education signals conscientiousness instead. So far, so good. But as I've said several times, in the real world education is also a signal of conformity. One of the main things a stack of degrees says about you is, "I uncomplainingly submit to social expectations."
http://econlog.econlib.org/archives/2012/04/signaling_versu.html

The argument in his 4/16 post is one of the better ones in favor of stability of the education status quo that I have heard. I liked John Roccia's comment as well. It definitely appears to me there are multiple worlds here and signaling vs. skills/learning matter differently in each.

@robrambusch I had vaguely heard of Demara, but never really looked into his story. His "expand into the power vacuum" concept is quite interesting. He must have had some impressive "people skills" (and might be a good person to bring up when talking to those who overvalue people skills ;-). Did you get any sense from the family friend if he was competent as well? If so, he seems like someone who was badly served by the emphasis on credentialism. Thanks for adding a personal touch to his story.